The two equations $3x+6y=15$ and $6x+12y=30$ have

For a pair of linear equations $a_{1}x+b_{1}y=c_1$ and $a_{2}x+b_{2}y=c_2$, check the ratio of coefficients:
$$\frac{a_1}{a_2}=\frac{3}{6}=\frac{1}{2}$$

$$\frac{b_1}{b_2}=\frac{6}{12}=\frac{1}{2}$$

$$\frac{c_1}{c_2}=\frac{15}{30}=\frac{1}{2}$$

Since $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$, the two lines are coincident, which means the system has an infinite number of solutions.